Particle Trapping in Axisymmetric Electron Holes

Electron orbits are calculated in solitary two-dimensional axisymmetric electrostatic potential structures, typical of plasma electron holes, in order to establish the conditions for the particles to remain trapped. Analytic calculations of the evolution of the parallel energy caused by the perturbing radial electric field (breaking magnetic-moment invariance) are shown to agree well with full numerical orbit integration Poincare plots. The predominant mechanism of detrapping is resonance between the gyro frequency in the parallel magnetic field and harmonics of the parallel bounce frequency. A region of phase-space adjacent to the trapped-passing boundary in parallel energy is generally stochastic because of island overlap of different harmonics, but except for very strong radial electric field perturbation, more deeply trapped orbits have well-defined islands and are permanently confined. A simple universal quantitative algorithm is given, and its results plotted as a function of magnetic field strength and hole radial scale-length, determining the phase space volume available to sustain the electron hole by depression of the permanently trapped distribution function.

电子轨道在等离子体电子空穴（plasma electron holes）的典型孤立二维轴对称静电势结构中进行计算，以确定粒子维持俘获的条件。由扰动径向电场（破坏磁矩不变性）引发的平行能量演化的解析计算结果，与完整数值轨道积分得到的庞加莱图（Poincare plot）吻合良好。脱俘获的主要机制为平行磁场中的回旋频率与平行反弹频率的谐波之间的共振。平行能量下紧邻俘获-通带边界的相空间区域通常因不同谐波的相空间岛重叠而呈现随机特性，但除极强的径向电场扰动外，更深俘获的轨道拥有明确的相空间岛，并会被永久约束。本文给出了一种简单的普适定量算法，其结果以磁场强度和电子空穴径向尺度为函数绘图，并通过压低永久俘获的粒子分布函数，确定了可维持该电子空穴的可用相空间体积。